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    "assumptions": "Let A ⊆ B(Hₐₜ) be the fixed unital C*-algebra obtained by adjoining the chosen shell-link unitaries to the atomic representation of the CAR algebra C, and then taking the norm-closed unital *-algebra they generate. Let Hτ = L²(C, τC) be the GNS Hilbert space of the normalized CAR trace τC. Let ρ be the specified representation obtained by pointed unitary transport of the tracial model.",
    "conclusion": "ρ is injective: for all a, b ∈ A, ρ(a) = ρ(b) implies a = b. In particular, ρ(a) = 0 implies a = 0.",
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        "step_id": "2",
        "text": "Apply it to the same family used to define A and ρ."
      }
    ],
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    "assumptions": "Let A ⊆ B(Hₐₜ) be the fixed unital C*-algebra obtained by adjoining the chosen shell-link unitaries to the atomic representation of the CAR algebra C, and then taking the norm-closed unital *-algebra they generate. Let Hτ = L²(C, τC) be the GNS Hilbert space of the normalized CAR trace τC. Let ρ be the specified representation obtained by pointed unitary transport of the tracial model.",
    "conclusion": "ρ is injective: for all a, b ∈ A, ρ(a) = ρ(b) implies a = b. In particular, ρ(a) = 0 implies a = 0.",
    "content_completeness": "CARD_CONTENT_COMPLETE",
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      "text": "theorem separableCounterexampleRepresentation_injective :\n    Function.Injective separableCounterexampleRepresentation :=\n  traceModelRepresentation_injective homogeneityShellFamily"
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